Analysis And Simulation Of The Elastic Buckling Of Plane Steel Frame With Three-layer And Three-span

With the high speed development of construction industry and the rise of emerging industrial technology, the steel structure has been paid attention increasingly, and become an important type of structures. Due to the low weight, high degree industrialization, short construction period, high comprehensive economic benefits and environmental efficiency, the structure has been widely applied in industrial, civil and national defense fields, such as multistorey steel frame plant, house, steel structure villa, hangar, gymnasium, exhibition hall and so on. The bucking of various steel structures has become a topical issue in the fields of solid mechanics and structural engineering, and the buckling of steel structure has already attracted broad attention of industry scholars. Therefore the detailed analysis of steel structure will make the stability theory perfect, and be of practical significance. Based on this, the elastic static and dynamic buckling of plane steel frame with three-layer and three-span are investigated by theoretical analysis and simulation in the present study.1. The current research of static and dynamic buckling of steel frame was introduced, and the method and conclusions are analyzed and summarized.2. The mode equations and the critical buckling Conditions of the plane steel frame with three-layer and three-span under the condition of no-sway and sway were obtained, and the buckling governing equation of the steel frame derived from Hamilton principle was solved. The buckling load of the steel frame was obtained by the expressions and scope of the effective length factors μ calculated from MATLAB.Theoretical results indicated that under the condition of static with sway and no-sway, the effective length factors decrease with the increase of stiffness ratio of beam. The factor μ of no-sway steel frame with fixed-end and hinged-end was0.5～0.94and0.7～1.0, respectively. the factor μ of sway steel frame with fixed-end and hinged-end was1.0～3.9and2.0～4.0. And, under the same ratio of beam rigidity, the factor with hinged-end column base was larger than that with fixed-ended column base.3. Based on Hamilton principle, the buckling governing equation of the steel frame considering the effect of stress wave was given. The critical buckling conditions and the mode equations of no-sway steel frame were acquired by using the initial boundary conditions and the constraint conditions of wave front. Using MATLAB software, the effective length factors μ and buckling parameters k1were obtained. Theoretical results indicated that the effective length factors of dynamic buckling increase and the buckling parameters decrease with the increase of the ratio of beam rigidity K. With the yield length lcr of steel column increasing continuously, the effective length factors increased and the buckling parameters decreased gradually. In addition, when the ratio of beam rigidity K increased, the rate of effective length coefficient change increased accordingly.4. The expression and scope of effective length factor μ were obtained by using the same principle above. The results exhibited that that the number of layers and spans of multi-story and multi-span steel frame has a certain influence on the effective length factors, and the numbers of layer has a greater influence.5. Using ANSYS software, the finite element model was established, which was consistent with the theoretical model. The static and dynamic buckling were simulated under concentrated load, uniformly distributed load and distributed load with fixed-end and hinged-end of steel frame. The results were essentially agree with the theoretical values. The errors of no-sway steel frame was less than0.4%. The errors of sway steel frame was within2%, and will decreases sharply when the ratio of beam rigidity K increased gradually. When K≥0.15, the errors are within2%. the results indicated that the simulation of the three-layer and three-span steel frame was effective.